Your housing provider can’t require that your assistance animal have special training or certification to be an assistance animal.
Some assistance animals have special training, some are trained by their owners, and some don’t have any training.
If your animal gives you help that you need because of your disability, it is an assistance animal under fair housing law, regardless of whether it has been trained.
Assistance animals that help you in your home are different from service animals. Service animals can go anywhere with you. Service animals must be specially trained. But animals that help you in your housing do not need special training.